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Prediction of partition coefficients of alkaloids in ionic liquids based aqueous biphasic systems using hybrid group method of data handling (GMDH) neural network
Journal of Molecular Liquids 191 (2014) 79–84
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Prediction of partition coefficients of alkaloids in ionic liquids based aqueous biphasic systems using hybrid group method of data handling (GMDH) neural network Shiva Abdolrahimi, Bahram Nasernejad ⁎, Gholamreza Pazuki Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
a r t i c l e
i n f o
Article history: Received 4 October 2013 Received in revised form 22 November 2013 Accepted 27 November 2013 Available online 10 December 2013 Keywords: Aqueous biphasic systems Ionic liquids Alkaloid Partition coefficient GMDH Modeling
a b s t r a c t In this study, a hybrid GMDH–neural network model was developed in order to predict partition coefficients of alkaloids in aqueous biphasic system using different ionic liquids with the same inorganic salt. In order to accomplish this modeling, feed's weight percent compositions along with slope of tie-line (STL), tie-line length (TLL) and difference of molecular weight of salt and Ionic liquid were taken as the inputs and the desired partition coefficients (K) were estimated. Furthermore, the data set was divided into two parts: 80% of the data points were used for training and 20% for testing. For evaluation of the model's performance, partition coefficients obtained from the GMDH model were compared with their experimental values using different statistical measures. The proposed model can successively correlate and predict K-values and result a great agreement with the experimental data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The separation and purification of biomolecules are of great industrial importance. This is mainly due to the fact that, the final cost of production is directly related to the separation processes involved. In the mid-1950s, Albertsson [1] proposed aqueous biphasic system (ABS) as a replacement to the conventional liquid–liquid extraction technique. As both phases are mainly composed of water, ABSs provide great compatible media for biomolecules. Since 1980, polymer-based ABSs have been extensively employed in separation processes as a mixture of two incompatible polymers or a polymer and a salting-out agent [2,3]. However, Rogers et al. [4] presented a novel system of ionic liquid (IL)-inorganic salt for the creation of ABS. Distinct physical and chemical properties of ILs such as negligible volatility, non-flammability, tunability and high selectivity make them interesting for industrial applications [5]. Moreover, the efficient application of ILs for separation and purification requires a thorough knowledge of molecular mechanism behind biomolecule's partitioning [6]. Consequently, modeling of partitioning process is of great scientific importance. The local composition based models [7–9] and the empirical correlation [10–12] are two applied methods for obtaining biomolecule's partition coefficient in polymer-based ABS. Recently, a new prediction method based on artificial neural networks systems (ANNs) has been developed for application in chemical engineering ⁎ Corresponding author. Tel.: +98 (021) 64543128; fax: +98 (021) 66405847. E-mail address: [email protected] (B. Nasernejad). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.11.033
for estimation of VLE and LLE data [13–18]. ANNs simulate neurons' function in the brain and they are mostly considered to be nonlinear and highly flexible universal approximators [19,20]. Nonetheless, its main drawback is that the detected dependencies are concealed behind neural network structure [21]. Contrarily, the group method of data handling (GMDH) mainly describes the functional structure of a model which is hidden in the empirical data [22]. GMDH was originated by the Ukrainian scientist Ivakhneko in 1968 and it has been improving and evolving over the past 40 years. GMDH is an analysis technique for establishing the nonlinear relationships between the system's inputs and outputs. GMDH is a typical inductive modeling method which has been applied to complicated systems in several fields such as modeling, predicting, data mining and system identification. Moreover, GMDH algorithms are high order polynomial networks which are mainly feed-forward and multi-layered neural networks [23]. In this concept, the nodes are hidden units and the activation polynomial coefficients are weights which are estimated by ordinary least square regression [23,24]. Kan and Lee used a neural network model for prediction of liquid– liquid phase equilibrium in polymer–salt aqueous biphasic system [25]. Moreover, partition coefficient of β-glucosidase in polymer–salt aqueous two-phase system was estimated by Gautam and Simon using artificial neural network model [26]. Also, Pazuki et al. used ANN as modeling method for prediction of partitioning coefficients of some biomolecules [27]. In another work, Pazuki and Seyfi proposed a hybrid GMDH neural network to modeling of penicillin G Acylase in polymer– salt aqueous two-phase systems [28].
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Due to IL's favorable properties, IL based ABSs have been considered as an efficient downstream processing method. Many biomolecules have been recovered and purified using IL based ABS. However, in most research studies the partition coefficients were reported quantitatively and not as a function of system's parameters [29–31]. Moreover, knowledge of the factors that influence this parameter and consequently its prediction is a novel field of study. Hence, there is a shortcoming in modeling biomolecule's partitioning in IL-based ABS and thus focusing on this field of study is of great scientific importance. Furthermore, these models can be a potent mean to gain an insight into more unknown extraction systems. In this work, a model for predicting partitioning data of alkaloids (caffeine and nicotine) in IL-based aqueous biphasic system was developed using the GMDH algorithm. Employing existing experimental data gathered by Freire et al. [29] the model was trained and the obtained data were compared with the experimental data in order to investigate the reliability of the proposed model.
2
1
xi
xj
6 2 6 xi xi xi x j 6 6 2 6 x j xi x j x j X¼6 2 2 6 6 xi x j xi x j xi x j 6 2 3 2 6 xi xi xi x j 4 2 2 3 x j xi x j x j a ¼ ½ a0
a1
a2
a3
2
xi x j
xi
2
xi x j 2
xi x j
2 2 xi x j 3 xi x j 3 xi x j
a4
3
xi
2
3
2
xj
2
xi x j
3 xj 3 3 xi x j xi x j 4 2 2 xi xi x j 2 2 4 xi x j x j
xi x j
7 7 7 7 7 7 7 7 7 7 5
ð7Þ
a5
ð8Þ
T
ð9Þ
b ¼ ðyY Þ
Thus we solve the system of equation in the following form [23,24]: N X n¼1
aX ¼
N X
ð10Þ
b:
n¼1
2. Material and methods
2.2. Hybrid GMDH–neural network
2.1. Group method of data handling
In the original approach of GMDH, all pair combinations of inputs are generated and thus they are fed to network's input layer. Consequently, the produced outputs of the input layer are classified and selected as the inputs of the next layer. This process is repeated continuously as long as each subsequent layer produces a better result than previous one [24]. Pair selection of inputs leads to exclusion of other variables' effect and thus when the system is highly non-linear less precise nodal
The relationship between the inputs and the output of a multiple inputs single output network can be estimated by Volterra–Kolmogorov– Gabor (VKG) polynomial [32]:
^ n ¼ a0 þ y
M X
a i xi þ
i¼1
M X M X
aij xi x j þ
i¼1 j¼1
M X M X M X
aij xi x j xk þ ::::
ð1Þ
i¼1 j¼1 k¼1
Where X = (x1, x2, …., xM) is the vector of input variables, a is the ^n is the predicted output. The general vector of weight coefficients and y equation in the form of VKG can be simplified to a partial quadratic polynomials consisting of only two variables [24]: ^n ¼ a0 þ a1 xin þ a2 xjn þ a3 xin xjn þ a4 x2in þ a5 x2jn y
1-Ethyl-3-methylimidazolium chloride [C2mim]Cl 1-Butyl-3-methylimidazolium chloride [C4mim]Cl
ð2Þ
When constructing a GMDH network, all combinations of the inputs are constructed and each layer consists of nodes taking a specific pair of inputs (xi,xj) as its source. Each node produces a set of coefficients, ai. Consequently, Eq. (2) is estimated based on the training set of data. ^n and the actual values are compared using Moreover, the predicted y testing set of data by estimation of mean square error [24]: N X ^n −yn Þ2 ðy
Table 1 Ionic liquids' structures and abbreviations used for partitioning of alkaloids.
1-Hexyl-3-methylimidazolium chloride [C6mim]Cl 1-Butyl-2,3-dimethylimidazolium chloride [C4C1mim]Cl
1-Benzyl-3-methylimidazolium chloride [C7H7mim]Cl
ð3Þ
1-Allyl-3-methylimidazolium chloride [amim]Cl
In order to determine the “best fit” values, the value e should be minimized, or in another word, the partial derivatives of Eq. (3) with respect to each constant ai are taken and set equal to zero [24]:
1-hydroxyethyl-3-methylimidazolium chloride [OHC2mim]Cl 1-Ethyl-3-methylimidazolium triflate [C2mim][CF3SO3]
e¼
n¼1
∂e ¼0 ∂ai
ð4Þ
Solving Eq. (4) leads to a system of equations that are solved by training set of date: h Y ¼ 1 xi T
X¼Y Y
xj
xi x j
2
xi
2
xj
i
ð5Þ
ð6Þ
1-Butyl-3-methylimidazolium methanesulfonate [C4mim][CH3SO3] 1-Ethyl-3-methylimidazolium acetate [C2mim][CH3CO2]
1-Butyl-3-methylimidazolium trifluroacetate [C4mim][CF3CO2]
S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
81
Table 2 Experimental partition coefficients of alkaloids in IL-based ABS as a function of feed's weight percent composition, STL and TLL at 298.15 K. Ionic liquid
a
CAFFEINE
a
NICOTINE
a
[C2mim]Cl [C4mim]Cl [C4C1mim]Cl [C6mim]Cl [C7mim]Cl [C8mim]Cl [amim]Cl [amim]Cl [OHC2mim]Cl [C7H7mim]Cl [C7H7mim]Cl [C2mim][CF3SO3] [C4mim][CF3SO3] [C2mim][CH3CO2] [C4mim]Br [C4mim][CH3SO3] [C4mim][CF3CO2] [C2mim]Cl [C2mim]Cl [C4mim]Cl [C4mim]Cl [C8mim]Cl [amim]Cl [C2mim][CF3SO3] [C4mim][CF3SO3] [C2mim][C2H5SO4] [C2mim][CH3CO2] [C4mim]Br [C4mim][CH3SO3] [C4mim][CF3CO2]
Feed's wt.% IL
K3PO4
25.185 24.361 25.127 24.921 25.066 25.068 24.262 44.817 39.963 25.123 49.962 24.996 24.996 25.172 24.822 24.917 24.785 25.292 40.093 25.569 49.957 25.01 24.945 24.983 25.08 24.185 24.933 25.046 24.998 24.933
14.962 14.923 15.08 14.856 15.166 15.073 15.293 15.193 15.049 14.925 14.883 14.891 15.352 14.931 15.085 15.09 15.475 14.778 15.129 14.882 15.159 15.079 15.198 15.124 14.957 16.381 15.571 14.937 14.979 14.779
STL
TLL
MWsalt − MWIL
K
−1.138 −1.2 −1.262 −1.45 −1.611 −1.699 −1.189 −1.298 −3.048 −1.701 −1.719 −2.991 −2.995 −0.993 −1.692 −1.306 −2.187 −1.099 −1.237 −1.216 −1.405 −1.717 −1.773 −3.027 −2.863 −1.743 −0.936 −1.686 −1.32 −2.124
43.386 44.493 47.966 45.907 44.417 36.784 42.842 81.148 63.673 43.036 86.458 61.973 70.428 48.132 45.396 38.919 56.984 43.583 73.95 47.673 87.41 36.597 44.833 63.646 65.409 45.78 48.787 45.3 38.511 53.478
65.64626 35.58626 23.56626 9.546261 −4.47374 −18.4937 53.63626 53.63626 49.64626 3.576261 3.576261 −47.9637 −76.0237 42.05626 −6.85374 −22.0537 −39.9637 65.64626 65.64626 35.58626 35.58626 −18.4937 53.63626 −47.9637 −76.0237 −24.0237 42.05626 −6.85374 −22.0537 −39.9637
46.1 49 99.6 44.1 37 38.2 29.4 32.3 98.9 42.62 90 25.1 30 66 30.4 16.6 41.8 52.7 58.7 82.1 95.5 32.1 59.3 67.9 79.6 22.8 66.9 47.3 32.1 74.2
Initial concentrations of caffeine and nicotine were, respectively, 2.6* 10−2 mol dm−3 and 2.5 *10−2 mol dm−3.
polynomials' estimation is resulted. In order to alleviate the problems associated with standard GMDH approach, a number of researchers have attempted to hybridize GMDH with some evolutionary optimization techniques. Among them, hybridization of GMDH with neural network is one of the promising techniques. In this method each node can
take any combination of input variables unless the polynomial's order exceeds two. Furthermore, the input of each node can cross over other layers and consequently the model's complexity is increased. Additionally, as the numbers of possible combinations among nodes are augmented the proposed model can better estimate the non-linearity
Table 3 Nodal expressions for hybrid GMDH–NN. Layer 1 w1 w2 w3 w4 w5 w6 w7 w8 w9
= = = = = = = = =
10.89x1 − 0.222x1x3 + 1.381x2x3 − 24.92x21 − 103.4x22 + 0.05169x23 0.6047x3 + 2.654x4 − 3.263x1x3 − 9.53x1x4 0.8306 + 0.8736x3 + 0.01796x5 − 6.711x1x3 + 0.01126x3x5 − 18.66x21 − 8.854 * 10−5x25 16.99x1 + 53.33x2x4 − 46.14x21 − 445.8x22 − 1.955x24 −25.33x1 + 7.69x4 + 0.04586x5 − 51.77x1x4 − 0.3256x1x5 + 196.3x21 + 6.448 * 10−5x25 −23.79 + 380.9x2 + 0.2035x3 + 51.36x4 − 652.9x2x4 − 819.6x22 + 0.02715x23 − 3.287x24 0.6819 − 0.7713x3 + 15.51x2x3 + 0.0422x2x5 + 0.1213x23 − 1.784 * 10−5x25 6.819x4 − 80.39x2x4 + 0.1443x2x5 − 0.01481x4x5 − 4.36 * 10−5x25 0.9949x3 + 5.028x4 + 2.131x3x4 − 0.007882x3x5 − 0.02959x4x5 + 0.5116x23
Layer 2 z1 z2 z3 z4 z5 z6
= = = = = =
−3.215 + 9.443w1 + 4.379w2 − 6.532w1w2 − 42.48w1w8 + 15.74w21 + 20.47w28 −1.68 − 9.798w1 + 0.4141w4 + 18.34w7 − 77.51w1w4 − 96.09w3w7 + 55.06w4w7 + 96.54w21 + 12.65w24 −1.928 − 2.281x3w2 + 0.4312x3w7 + 13.3w2w7 − 1.446w22 − 5.632w27 − 0.1576x23 3.198w4 − 3.808w5 + 1.815w9 + 3.39w4w5 − 8.136w4w9 + 15.05w5w9 − 5.881w25 − 4.723w29 −2.889 + 9.546x4 + 4.071w3 − 2.824w5 − 7.13w3w5 − 4.188x4w5 − 6.204x24 + 9.5w25 −3.425w4 + 4.261w6 + 22.26w4w6 − 23.93w6w8 − 6.026w24 − 3.81w26 + 11.66w28
Layer 3 u1 = 0.5788w2 − 0.7715z2 + 1.061z4 − 6.926w2z2 + 9.969z2z4 + 1.783w22 − 4.638z24 u2 = −0.3917 − 3.715z1 + 3.447z3 + 2.917z6 + 10.81z1z3 − 4.29z1z6 + 3.176z3z6 − 9.521z23 − 1.505z26 u3 = −0.08059 + 0.5958z5 + 0.8534z4 + 3.886z4z5 + 4.628z5z6 + 2.137z4z6 − 4.29z25 − 3.669z24 − 2.906z26 Output layer 0 K ¼ −0:08528−0:6978u1 −0:3122u2 þ 2:25u3 þ 6:361u1 u2 −4:226u1 u3 −4:749u2 u3 þ 0:4305u22 þ 2:061u23 K ¼ 100 ILðmolÞ x1 ¼ solvent ðgr Þ
salt ðmolÞ x2 ¼ solvent ðgrÞ
x3 ¼ STL x4 ¼ TLL=100
x5 ¼ MW salt −MW IL
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S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
of the system. Thus, predicted output of hybrid GMDH–NN can be estimated as follows:
^ n ¼ a0 þ y
M X i¼1
a i xi þ
M X M X
aij xi x j :
ð12Þ
i¼1 j¼1
3. Results and discussions
difference between molecular weight of salt and IL. Thus, weight fraction composition of IL and K3PO4 in the feed (IL and K3PO4 wt.%) along with STL, TLL and difference of molecular weight of K3PO4 and IL have been selected as the inputs and the partition coefficient of alkaloids (K) is the desired output of the network. This partition coefficient in aqueous biphasic systems is defined as: K bio ¼
In this study, hybrid GMDH-type neural network was developed for prediction of partition coefficients of two main alkaloids – caffeine and nicotine – in IL-based aqueous biphasic system. The experimental data employed in this study were obtained from the work of Freire et al. [29], which mainly focused on the ability of several distinct ionic liquids as constituents of the extraction media along with same inorganic salt (K 3PO4). Table 1 demonstrates the structures and abbreviations of ILs used for ABS. The experimental data contain 30 points while 80% of these data points were used for training and 20% for testing. In Table 2, the overall experimental data set are reported based on the feed's composition, tie-line's slope (STL), tie-line length (TLL) and
C top bio C bottom bio
ð12Þ
Where C is the concentration of biomolecule and subscripts “top” and “bottom” stand for the top and bottom phase, respectively. When using the reported data in the original work of Freire et al. [29] (Table 2), some modifications are required. The first modification is aiming at removing the influence of divergences in weight percents of ionic liquids in the feed which could be resulting from the different molecular weights of the dissimilar ILs. Thus, weight fraction compositions in the feed are converted to the molality units (mol of solute per g of solvent). Furthermore, in the original reported data full extraction efficiencies of alkaloids as a function of inputs were also stated. However, the model is unable to predict fixed value for the output while the input
Fig. 1. A schematic diagram of proposed hybrid GMDH–NN.
S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
83
Table 4 Comparison between hybrid and original GMDH with computed average absolute error (AAD%). K′ value(a)
K′ value(a)
No.
Exp(b)
Hybrid Predicted
%AAD
Predicted
%AAD
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total
0.461 0.49 0.996 0.441 0.37 0.382 0.294 0.323 0.989 0.4262 0.9 0.251 0.3 0.66 0.304
0.4663 0.5150 0.9902 0.5018 0.3444 0.3436 0.2803 0.3279 1.0069 0.4331 0.9151 0.2713 0.3513 0.6655 0.3658
1.1497 5.0931 0.5774 13.776 6.9311 10.051 4.6612 1.5068 1.8109 1.6288 1.6793 8.0737 17.099 0.84 20.360
0.4972 0.4892 0.6354 0.5546 0.4605 0.3013 0.4581 0.5231 0.9769 0.5228 1.0027 0.4157 0.4384 0.8599 0.4575
7.848 0.160 36.20 25.76 24.45 21.13 55.81 61.94 1.223 22.67 11.42 65.61 46.13 30.29 50.50
(a) (b)
Original
No.
Exp(b)
Hybrid Predicted
%AAD
Predicted
%AAD
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0.166 0.418 0.527 0.587 0.821 0.955 0.321 0.593 0.679 0.796 0.228 0.669 0.473 0.321 0.742
0.1506 0.3824 0.4958 0.6315 0.8276 0.9607 0.3473 0.5455 0.6013 0.7417 0.1827 0.6533 0.4403 0.2013 0.4847
9.2934 8.5225 5.9201 7.5792 0.8015 0.5996 8.1779 8.0120 11.4402 6.8215 19.8689 2.3416 6.9118 37.3024 34.6679 8.7833
0.0224 0.6160 0.5035 0.4572 0.6474 0.8843 0.3028 0.4801 0.4876 0.6729 0.2125 0.7814 0.5198 0.1267 0.7025
86.49 47.39 4.468 22.11 21.15 7.400 5.678 19.04 28.19 15.46 6.789 16.80 9.892 60.53 5.322 27.262
Original
K′ = K/100. Experimental K′ value.
Table 5 Model statistics for hybrid GMDH–NN for predicting alkaloid's partition coefficients in IL-based ABS. Statistics
Training
Testing
0.9964
0.9070
0.0349
0.1649
2 . N N MSE ¼ ∑ Y imodel −Y actual i
0.0012
0.0271
. N MAD ¼ ∑Y imodel −Y actual N i
0.0283
0.1365
"
2 . N 2 ∑ Y actual R2 ¼ 1− ∑ Y imodel −Y actual i i
Absolute fraction of variance (R2)
"
Root mean square error (RMSE)
N
i¼1
i¼1
N
#
RMSE ¼ ∑ Y imodel −Y actual i
2
, #1=2 N
i¼1
Mean square error (MSE)
i¼1
Mean absolute deviation (MAD)
i¼1
Predicted K'-value
a
Partitioning Coefficient
a 1.2 1 0.8 0.6 0.4 0.2
1.2
Actual Learning
1
Predicted
0.8 0.6 0.4 0.2 0 0
5
10
0 0
0.2
0.4
0.6
0.8
1
1.2
Predicted K'-value
b
b Partitioning Coefficient
Actual K'-value 1.2 1 0.8 0.6 0.4 0.2 0
15
20
25
30
Data Number 1.2
Actual Learning
1
Predicted
0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
1.2
Actual K'-value Fig. 2. Predicted partition coefficients plotted against actual data (K′ = K/100). (a) Hybrid GMDH–NN and (b) original GMDH network.
0
5
10
15
20
25
30
Data Number Fig. 3. Predicted partition coefficients (K′ = K/100) plotted against data number. (a) Hybrid GMDH–NN and (b) original GMDH network.
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S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
variables are changing. Thus, in the second modification these points are omitted from the data set. In order to unify the order of magnitude of the inputs and outputs, some modifications are performed on them. These modifications are stated in Table 3. In this study, the structure of hybrid GMDH–neural network model was developed with 3 neural inputs in 4 layers, as shown in schematic Fig. 1. As can be seen from the figure, the proposed model has one input layer, two middle layer and one output layer. Moreover, the figure clearly shows some cross overs between nodes in different layers which is the distinct characteristic of hybrid GMDH–NN model. Generated functions corresponding to each node in each layer along with total correlation function are represented in Table 3. The actual and predicted results together with related Average Absolute Deviations Percent (% AAD) are reported in Table 4. Moreover, Table 5 demonstrates the differences between original and hybrid GMDH model. The general formula for the calculation of %AAD is given in Eq. (13):
%AAD ¼
N model 100 X −Y actual Y i i actual N i¼1 Yi
ð13Þ
Table 5 clearly shows the reliability and accuracy of the proposed hybrid GMDH–NN model in predicting partitioning of alkaloids in IL-based ABS in comparison with original one. Moreover, the experimental and predicted K-values are compared in Figs. 2 and 3. As can be observed from the figures, the results of the proposed model are in good agreement with the experimental data as many of the data points fall very close to diagonal line. However, original GMDH is unable to predict the variation of K-value as the function of inputs. Some statistical measures can be used for determining the model's accuracy and reliability. These statistical values can be defined as shown in the Table 4 and their values are calculated based on the output of the network. 4. Conclusion As it was observed, hybrid GMDH–NN was used in order to estimate partition coefficients of two alkaloids in ABS based on different ILs and the same inorganic salt. The model was developed in 4 layers with 3 inputs in each layer. Schematic diagram of the proposed model showed some cross overs between layers which are, as stated, the distinct characteristic of hybrid GMDH–NN. Furthermore, comparison of the estimated K-values with experimental results, as demonstrated in tables and figures, showed excellent agreements among them. Some statistical measures were also used in order to estimate the model's accuracy. Their calculated values fitted well among their standard values and thus proposing reliability of the model. Moreover, %AAD was calculated to be 8.78% which
was a desired value in statistical measures. Hence, the closeness of the predicted and experimental K-values demonstrates that the model can efficiently predict alkaloid's partitioning in IL-based ABS at 298.15 K. The proposed model shows how different process variables influence K-values of alkaloid in IL-based ABS. Indeed, changing the type of ABS system would change the final equation but the core structure of the model is unchanged. Thus, the proposed model gives an insight into the influencing parameters and can be used as the basis for modeling of other types of ABS. References [1] P.A. Albertsson, Partitioning of Cell Particles and Macromolecules, Third ed. Wiley-Interscience, New York, 1986. [2] R.K. Scopes, Protein Purification: Principles and Practice, Third ed. Springer-Verlag, Berlin, 1994. [3] B.Y. Zaslavsky, Aqueous Two-Phase Partitioning—Physical Chemistry and Bioanalytical Applications, Marcel Dekker, New York, 1995. [4] K.E. Gutowski, G.A. Broker, H.D. Willauer, J.G. Huddleston, R.P. Swatloski, J.D. Holbrey, R.D. Rogers, J. Am. Chem. Soc. 125 (2003) 6632. [5] M.G. Freire, A.M. Claudio, J.M.M. Araujo, A.P. Coutinho, I.M. Marrucho, I.M. Canongia Lopes, P.N. Rebelo, Soc. Rev. 41 (2012) 4966. [6] S. Dreyer, P. Salim, U. Kragl, Biochem. Eng. J. 46 (2009) 176. [7] P.P. Madeira, X. Xu, J.A. Teixeira, E.A. Macedo, Biochem. Eng. J. 24 (2005) 147. [8] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Z. Phys. Chem. 223 (2009) 263. [9] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Ind. Eng. Chem. Res. 48 (2009) 4109. [10] A.D. Diamond, J.T. Hsu, Biotechnol. Bioeng. 34 (1989) 1000. [11] A.D. Diamond, J.T. Hsu, J. Chromatogr. B 513 (1990) 137. [12] A.D. Diamond, J.T. Hsu, AlChE Symp. Ser. 88 (1992) 105. [13] S. Ganguly, J. Comput. Chem. Eng. 27 (2003) 1445. [14] S. Ketabchi, H. Ghanadzadeh, A. Ghanadzadeh, S. Fallahi, M. Ganji, J. Chem. Thermodyn. 42 (2010) 1352. [15] S.Z. Reyhani, H. Ghanadzadeh, L. Puigjaner, F. Recances, J. Ind. Eng. Chem. Res. 48 (2009) 2129. [16] F.S. Mjalli, J. Chem. Eng. Sci. 60 (2005) 239. [17] J.S. Torrecilla, M. Deetlefs, J. Chem. Phys. 10 (2008) 5114. [18] S. Bogdan, D. Gosak, D. Vasic-Racki, Comput. J. Chem. Eng. 19 (1995) 791. [19] J. Park, I. Sandberg, J. Neural Comput. 3 (1991) 246. [20] M.J.D. Powell, in: J.C. Mason, M.G. Cox (Eds.), Radial Basis Functions for Multivariable Interpolation: A Review in Algorithms for Approximation, Clarendon Press, Oxford, UK, 1987, p. 143. [21] N. Nariman-Zadeh, A. Jamali, in: J. Drchal, J. Koutnik (Eds.), Proceedings of the International Workshop on Inductive Modelling, Czech Technical University, Prague, Czech Republic, 2007, p. 96. [22] A.G. Ivakhnenko, IEEE Trans. Syst. Man Cybern. 1 (1971) 364. [23] H. Ghanadzadeh, M. Ganji, S. Fallahi, Appl. Math. Model. 36 (2012) 4096. [24] G.C. Onwubolu, Hybrid Self-Organizing Modeling Systems, Springer, Berlin, 2009. [25] P. Kan, C.J. Lee, Ind. Eng. Chem. Res. 35 (1996) 2015. [26] G. Gautam, L. Simon, Chem. Eng. Commun. 194 (2007) 117. [27] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Part. Sci. Technol. 28 (2010) 67. [28] G.R. Pazuki, S. Seyfi Kakhki, J. Mol. Liq. 188 (2013) 133. [29] M.G. Freire, C.M.S.S. Neves, I.M. Marrucho, J.N. Lopes, L.P. Rebelo, J.A.P. Coutinho, Green Chem. 12 (2010) 1715. [30] C.M.S.S. Neves, S.P.M. Ventura, M.G. Freire, I.M. Marrucho, J.A.P. Coutinho, J. Phys. Chem. B 113 (2009) 5194. [31] S.P.M. Ventura, C.M.S.S. Neves, M.G. Freire, I.M. Marrucho, J. Oliveira, J.A.P. Coutinho, J. Phys. Chem. B 113 (2009) 9304. [32] A.G. Ivakhnenko, Sov. Autom. Control 13 (1966) 43.
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Prediction of partition coefficients of alkaloids in ionic liquids based aqueous biphasic systems using hybrid group method of data handling (GMDH) neural network Shiva Abdolrahimi, Bahram Nasernejad ⁎, Gholamreza Pazuki Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
a r t i c l e
i n f o
Article history: Received 4 October 2013 Received in revised form 22 November 2013 Accepted 27 November 2013 Available online 10 December 2013 Keywords: Aqueous biphasic systems Ionic liquids Alkaloid Partition coefficient GMDH Modeling
a b s t r a c t In this study, a hybrid GMDH–neural network model was developed in order to predict partition coefficients of alkaloids in aqueous biphasic system using different ionic liquids with the same inorganic salt. In order to accomplish this modeling, feed's weight percent compositions along with slope of tie-line (STL), tie-line length (TLL) and difference of molecular weight of salt and Ionic liquid were taken as the inputs and the desired partition coefficients (K) were estimated. Furthermore, the data set was divided into two parts: 80% of the data points were used for training and 20% for testing. For evaluation of the model's performance, partition coefficients obtained from the GMDH model were compared with their experimental values using different statistical measures. The proposed model can successively correlate and predict K-values and result a great agreement with the experimental data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The separation and purification of biomolecules are of great industrial importance. This is mainly due to the fact that, the final cost of production is directly related to the separation processes involved. In the mid-1950s, Albertsson [1] proposed aqueous biphasic system (ABS) as a replacement to the conventional liquid–liquid extraction technique. As both phases are mainly composed of water, ABSs provide great compatible media for biomolecules. Since 1980, polymer-based ABSs have been extensively employed in separation processes as a mixture of two incompatible polymers or a polymer and a salting-out agent [2,3]. However, Rogers et al. [4] presented a novel system of ionic liquid (IL)-inorganic salt for the creation of ABS. Distinct physical and chemical properties of ILs such as negligible volatility, non-flammability, tunability and high selectivity make them interesting for industrial applications [5]. Moreover, the efficient application of ILs for separation and purification requires a thorough knowledge of molecular mechanism behind biomolecule's partitioning [6]. Consequently, modeling of partitioning process is of great scientific importance. The local composition based models [7–9] and the empirical correlation [10–12] are two applied methods for obtaining biomolecule's partition coefficient in polymer-based ABS. Recently, a new prediction method based on artificial neural networks systems (ANNs) has been developed for application in chemical engineering ⁎ Corresponding author. Tel.: +98 (021) 64543128; fax: +98 (021) 66405847. E-mail address: [email protected] (B. Nasernejad). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.11.033
for estimation of VLE and LLE data [13–18]. ANNs simulate neurons' function in the brain and they are mostly considered to be nonlinear and highly flexible universal approximators [19,20]. Nonetheless, its main drawback is that the detected dependencies are concealed behind neural network structure [21]. Contrarily, the group method of data handling (GMDH) mainly describes the functional structure of a model which is hidden in the empirical data [22]. GMDH was originated by the Ukrainian scientist Ivakhneko in 1968 and it has been improving and evolving over the past 40 years. GMDH is an analysis technique for establishing the nonlinear relationships between the system's inputs and outputs. GMDH is a typical inductive modeling method which has been applied to complicated systems in several fields such as modeling, predicting, data mining and system identification. Moreover, GMDH algorithms are high order polynomial networks which are mainly feed-forward and multi-layered neural networks [23]. In this concept, the nodes are hidden units and the activation polynomial coefficients are weights which are estimated by ordinary least square regression [23,24]. Kan and Lee used a neural network model for prediction of liquid– liquid phase equilibrium in polymer–salt aqueous biphasic system [25]. Moreover, partition coefficient of β-glucosidase in polymer–salt aqueous two-phase system was estimated by Gautam and Simon using artificial neural network model [26]. Also, Pazuki et al. used ANN as modeling method for prediction of partitioning coefficients of some biomolecules [27]. In another work, Pazuki and Seyfi proposed a hybrid GMDH neural network to modeling of penicillin G Acylase in polymer– salt aqueous two-phase systems [28].
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Due to IL's favorable properties, IL based ABSs have been considered as an efficient downstream processing method. Many biomolecules have been recovered and purified using IL based ABS. However, in most research studies the partition coefficients were reported quantitatively and not as a function of system's parameters [29–31]. Moreover, knowledge of the factors that influence this parameter and consequently its prediction is a novel field of study. Hence, there is a shortcoming in modeling biomolecule's partitioning in IL-based ABS and thus focusing on this field of study is of great scientific importance. Furthermore, these models can be a potent mean to gain an insight into more unknown extraction systems. In this work, a model for predicting partitioning data of alkaloids (caffeine and nicotine) in IL-based aqueous biphasic system was developed using the GMDH algorithm. Employing existing experimental data gathered by Freire et al. [29] the model was trained and the obtained data were compared with the experimental data in order to investigate the reliability of the proposed model.
2
1
xi
xj
6 2 6 xi xi xi x j 6 6 2 6 x j xi x j x j X¼6 2 2 6 6 xi x j xi x j xi x j 6 2 3 2 6 xi xi xi x j 4 2 2 3 x j xi x j x j a ¼ ½ a0
a1
a2
a3
2
xi x j
xi
2
xi x j 2
xi x j
2 2 xi x j 3 xi x j 3 xi x j
a4
3
xi
2
3
2
xj
2
xi x j
3 xj 3 3 xi x j xi x j 4 2 2 xi xi x j 2 2 4 xi x j x j
xi x j
7 7 7 7 7 7 7 7 7 7 5
ð7Þ
a5
ð8Þ
T
ð9Þ
b ¼ ðyY Þ
Thus we solve the system of equation in the following form [23,24]: N X n¼1
aX ¼
N X
ð10Þ
b:
n¼1
2. Material and methods
2.2. Hybrid GMDH–neural network
2.1. Group method of data handling
In the original approach of GMDH, all pair combinations of inputs are generated and thus they are fed to network's input layer. Consequently, the produced outputs of the input layer are classified and selected as the inputs of the next layer. This process is repeated continuously as long as each subsequent layer produces a better result than previous one [24]. Pair selection of inputs leads to exclusion of other variables' effect and thus when the system is highly non-linear less precise nodal
The relationship between the inputs and the output of a multiple inputs single output network can be estimated by Volterra–Kolmogorov– Gabor (VKG) polynomial [32]:
^ n ¼ a0 þ y
M X
a i xi þ
i¼1
M X M X
aij xi x j þ
i¼1 j¼1
M X M X M X
aij xi x j xk þ ::::
ð1Þ
i¼1 j¼1 k¼1
Where X = (x1, x2, …., xM) is the vector of input variables, a is the ^n is the predicted output. The general vector of weight coefficients and y equation in the form of VKG can be simplified to a partial quadratic polynomials consisting of only two variables [24]: ^n ¼ a0 þ a1 xin þ a2 xjn þ a3 xin xjn þ a4 x2in þ a5 x2jn y
1-Ethyl-3-methylimidazolium chloride [C2mim]Cl 1-Butyl-3-methylimidazolium chloride [C4mim]Cl
ð2Þ
When constructing a GMDH network, all combinations of the inputs are constructed and each layer consists of nodes taking a specific pair of inputs (xi,xj) as its source. Each node produces a set of coefficients, ai. Consequently, Eq. (2) is estimated based on the training set of data. ^n and the actual values are compared using Moreover, the predicted y testing set of data by estimation of mean square error [24]: N X ^n −yn Þ2 ðy
Table 1 Ionic liquids' structures and abbreviations used for partitioning of alkaloids.
1-Hexyl-3-methylimidazolium chloride [C6mim]Cl 1-Butyl-2,3-dimethylimidazolium chloride [C4C1mim]Cl
1-Benzyl-3-methylimidazolium chloride [C7H7mim]Cl
ð3Þ
1-Allyl-3-methylimidazolium chloride [amim]Cl
In order to determine the “best fit” values, the value e should be minimized, or in another word, the partial derivatives of Eq. (3) with respect to each constant ai are taken and set equal to zero [24]:
1-hydroxyethyl-3-methylimidazolium chloride [OHC2mim]Cl 1-Ethyl-3-methylimidazolium triflate [C2mim][CF3SO3]
e¼
n¼1
∂e ¼0 ∂ai
ð4Þ
Solving Eq. (4) leads to a system of equations that are solved by training set of date: h Y ¼ 1 xi T
X¼Y Y
xj
xi x j
2
xi
2
xj
i
ð5Þ
ð6Þ
1-Butyl-3-methylimidazolium methanesulfonate [C4mim][CH3SO3] 1-Ethyl-3-methylimidazolium acetate [C2mim][CH3CO2]
1-Butyl-3-methylimidazolium trifluroacetate [C4mim][CF3CO2]
S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
81
Table 2 Experimental partition coefficients of alkaloids in IL-based ABS as a function of feed's weight percent composition, STL and TLL at 298.15 K. Ionic liquid
a
CAFFEINE
a
NICOTINE
a
[C2mim]Cl [C4mim]Cl [C4C1mim]Cl [C6mim]Cl [C7mim]Cl [C8mim]Cl [amim]Cl [amim]Cl [OHC2mim]Cl [C7H7mim]Cl [C7H7mim]Cl [C2mim][CF3SO3] [C4mim][CF3SO3] [C2mim][CH3CO2] [C4mim]Br [C4mim][CH3SO3] [C4mim][CF3CO2] [C2mim]Cl [C2mim]Cl [C4mim]Cl [C4mim]Cl [C8mim]Cl [amim]Cl [C2mim][CF3SO3] [C4mim][CF3SO3] [C2mim][C2H5SO4] [C2mim][CH3CO2] [C4mim]Br [C4mim][CH3SO3] [C4mim][CF3CO2]
Feed's wt.% IL
K3PO4
25.185 24.361 25.127 24.921 25.066 25.068 24.262 44.817 39.963 25.123 49.962 24.996 24.996 25.172 24.822 24.917 24.785 25.292 40.093 25.569 49.957 25.01 24.945 24.983 25.08 24.185 24.933 25.046 24.998 24.933
14.962 14.923 15.08 14.856 15.166 15.073 15.293 15.193 15.049 14.925 14.883 14.891 15.352 14.931 15.085 15.09 15.475 14.778 15.129 14.882 15.159 15.079 15.198 15.124 14.957 16.381 15.571 14.937 14.979 14.779
STL
TLL
MWsalt − MWIL
K
−1.138 −1.2 −1.262 −1.45 −1.611 −1.699 −1.189 −1.298 −3.048 −1.701 −1.719 −2.991 −2.995 −0.993 −1.692 −1.306 −2.187 −1.099 −1.237 −1.216 −1.405 −1.717 −1.773 −3.027 −2.863 −1.743 −0.936 −1.686 −1.32 −2.124
43.386 44.493 47.966 45.907 44.417 36.784 42.842 81.148 63.673 43.036 86.458 61.973 70.428 48.132 45.396 38.919 56.984 43.583 73.95 47.673 87.41 36.597 44.833 63.646 65.409 45.78 48.787 45.3 38.511 53.478
65.64626 35.58626 23.56626 9.546261 −4.47374 −18.4937 53.63626 53.63626 49.64626 3.576261 3.576261 −47.9637 −76.0237 42.05626 −6.85374 −22.0537 −39.9637 65.64626 65.64626 35.58626 35.58626 −18.4937 53.63626 −47.9637 −76.0237 −24.0237 42.05626 −6.85374 −22.0537 −39.9637
46.1 49 99.6 44.1 37 38.2 29.4 32.3 98.9 42.62 90 25.1 30 66 30.4 16.6 41.8 52.7 58.7 82.1 95.5 32.1 59.3 67.9 79.6 22.8 66.9 47.3 32.1 74.2
Initial concentrations of caffeine and nicotine were, respectively, 2.6* 10−2 mol dm−3 and 2.5 *10−2 mol dm−3.
polynomials' estimation is resulted. In order to alleviate the problems associated with standard GMDH approach, a number of researchers have attempted to hybridize GMDH with some evolutionary optimization techniques. Among them, hybridization of GMDH with neural network is one of the promising techniques. In this method each node can
take any combination of input variables unless the polynomial's order exceeds two. Furthermore, the input of each node can cross over other layers and consequently the model's complexity is increased. Additionally, as the numbers of possible combinations among nodes are augmented the proposed model can better estimate the non-linearity
Table 3 Nodal expressions for hybrid GMDH–NN. Layer 1 w1 w2 w3 w4 w5 w6 w7 w8 w9
= = = = = = = = =
10.89x1 − 0.222x1x3 + 1.381x2x3 − 24.92x21 − 103.4x22 + 0.05169x23 0.6047x3 + 2.654x4 − 3.263x1x3 − 9.53x1x4 0.8306 + 0.8736x3 + 0.01796x5 − 6.711x1x3 + 0.01126x3x5 − 18.66x21 − 8.854 * 10−5x25 16.99x1 + 53.33x2x4 − 46.14x21 − 445.8x22 − 1.955x24 −25.33x1 + 7.69x4 + 0.04586x5 − 51.77x1x4 − 0.3256x1x5 + 196.3x21 + 6.448 * 10−5x25 −23.79 + 380.9x2 + 0.2035x3 + 51.36x4 − 652.9x2x4 − 819.6x22 + 0.02715x23 − 3.287x24 0.6819 − 0.7713x3 + 15.51x2x3 + 0.0422x2x5 + 0.1213x23 − 1.784 * 10−5x25 6.819x4 − 80.39x2x4 + 0.1443x2x5 − 0.01481x4x5 − 4.36 * 10−5x25 0.9949x3 + 5.028x4 + 2.131x3x4 − 0.007882x3x5 − 0.02959x4x5 + 0.5116x23
Layer 2 z1 z2 z3 z4 z5 z6
= = = = = =
−3.215 + 9.443w1 + 4.379w2 − 6.532w1w2 − 42.48w1w8 + 15.74w21 + 20.47w28 −1.68 − 9.798w1 + 0.4141w4 + 18.34w7 − 77.51w1w4 − 96.09w3w7 + 55.06w4w7 + 96.54w21 + 12.65w24 −1.928 − 2.281x3w2 + 0.4312x3w7 + 13.3w2w7 − 1.446w22 − 5.632w27 − 0.1576x23 3.198w4 − 3.808w5 + 1.815w9 + 3.39w4w5 − 8.136w4w9 + 15.05w5w9 − 5.881w25 − 4.723w29 −2.889 + 9.546x4 + 4.071w3 − 2.824w5 − 7.13w3w5 − 4.188x4w5 − 6.204x24 + 9.5w25 −3.425w4 + 4.261w6 + 22.26w4w6 − 23.93w6w8 − 6.026w24 − 3.81w26 + 11.66w28
Layer 3 u1 = 0.5788w2 − 0.7715z2 + 1.061z4 − 6.926w2z2 + 9.969z2z4 + 1.783w22 − 4.638z24 u2 = −0.3917 − 3.715z1 + 3.447z3 + 2.917z6 + 10.81z1z3 − 4.29z1z6 + 3.176z3z6 − 9.521z23 − 1.505z26 u3 = −0.08059 + 0.5958z5 + 0.8534z4 + 3.886z4z5 + 4.628z5z6 + 2.137z4z6 − 4.29z25 − 3.669z24 − 2.906z26 Output layer 0 K ¼ −0:08528−0:6978u1 −0:3122u2 þ 2:25u3 þ 6:361u1 u2 −4:226u1 u3 −4:749u2 u3 þ 0:4305u22 þ 2:061u23 K ¼ 100 ILðmolÞ x1 ¼ solvent ðgr Þ
salt ðmolÞ x2 ¼ solvent ðgrÞ
x3 ¼ STL x4 ¼ TLL=100
x5 ¼ MW salt −MW IL
82
S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
of the system. Thus, predicted output of hybrid GMDH–NN can be estimated as follows:
^ n ¼ a0 þ y
M X i¼1
a i xi þ
M X M X
aij xi x j :
ð12Þ
i¼1 j¼1
3. Results and discussions
difference between molecular weight of salt and IL. Thus, weight fraction composition of IL and K3PO4 in the feed (IL and K3PO4 wt.%) along with STL, TLL and difference of molecular weight of K3PO4 and IL have been selected as the inputs and the partition coefficient of alkaloids (K) is the desired output of the network. This partition coefficient in aqueous biphasic systems is defined as: K bio ¼
In this study, hybrid GMDH-type neural network was developed for prediction of partition coefficients of two main alkaloids – caffeine and nicotine – in IL-based aqueous biphasic system. The experimental data employed in this study were obtained from the work of Freire et al. [29], which mainly focused on the ability of several distinct ionic liquids as constituents of the extraction media along with same inorganic salt (K 3PO4). Table 1 demonstrates the structures and abbreviations of ILs used for ABS. The experimental data contain 30 points while 80% of these data points were used for training and 20% for testing. In Table 2, the overall experimental data set are reported based on the feed's composition, tie-line's slope (STL), tie-line length (TLL) and
C top bio C bottom bio
ð12Þ
Where C is the concentration of biomolecule and subscripts “top” and “bottom” stand for the top and bottom phase, respectively. When using the reported data in the original work of Freire et al. [29] (Table 2), some modifications are required. The first modification is aiming at removing the influence of divergences in weight percents of ionic liquids in the feed which could be resulting from the different molecular weights of the dissimilar ILs. Thus, weight fraction compositions in the feed are converted to the molality units (mol of solute per g of solvent). Furthermore, in the original reported data full extraction efficiencies of alkaloids as a function of inputs were also stated. However, the model is unable to predict fixed value for the output while the input
Fig. 1. A schematic diagram of proposed hybrid GMDH–NN.
S. Abdolrahimi et al. / Journal of Molecular Liquids 191 (2014) 79–84
83
Table 4 Comparison between hybrid and original GMDH with computed average absolute error (AAD%). K′ value(a)
K′ value(a)
No.
Exp(b)
Hybrid Predicted
%AAD
Predicted
%AAD
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total
0.461 0.49 0.996 0.441 0.37 0.382 0.294 0.323 0.989 0.4262 0.9 0.251 0.3 0.66 0.304
0.4663 0.5150 0.9902 0.5018 0.3444 0.3436 0.2803 0.3279 1.0069 0.4331 0.9151 0.2713 0.3513 0.6655 0.3658
1.1497 5.0931 0.5774 13.776 6.9311 10.051 4.6612 1.5068 1.8109 1.6288 1.6793 8.0737 17.099 0.84 20.360
0.4972 0.4892 0.6354 0.5546 0.4605 0.3013 0.4581 0.5231 0.9769 0.5228 1.0027 0.4157 0.4384 0.8599 0.4575
7.848 0.160 36.20 25.76 24.45 21.13 55.81 61.94 1.223 22.67 11.42 65.61 46.13 30.29 50.50
(a) (b)
Original
No.
Exp(b)
Hybrid Predicted
%AAD
Predicted
%AAD
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0.166 0.418 0.527 0.587 0.821 0.955 0.321 0.593 0.679 0.796 0.228 0.669 0.473 0.321 0.742
0.1506 0.3824 0.4958 0.6315 0.8276 0.9607 0.3473 0.5455 0.6013 0.7417 0.1827 0.6533 0.4403 0.2013 0.4847
9.2934 8.5225 5.9201 7.5792 0.8015 0.5996 8.1779 8.0120 11.4402 6.8215 19.8689 2.3416 6.9118 37.3024 34.6679 8.7833
0.0224 0.6160 0.5035 0.4572 0.6474 0.8843 0.3028 0.4801 0.4876 0.6729 0.2125 0.7814 0.5198 0.1267 0.7025
86.49 47.39 4.468 22.11 21.15 7.400 5.678 19.04 28.19 15.46 6.789 16.80 9.892 60.53 5.322 27.262
Original
K′ = K/100. Experimental K′ value.
Table 5 Model statistics for hybrid GMDH–NN for predicting alkaloid's partition coefficients in IL-based ABS. Statistics
Training
Testing
0.9964
0.9070
0.0349
0.1649
2 . N N MSE ¼ ∑ Y imodel −Y actual i
0.0012
0.0271
. N MAD ¼ ∑Y imodel −Y actual N i
0.0283
0.1365
"
2 . N 2 ∑ Y actual R2 ¼ 1− ∑ Y imodel −Y actual i i
Absolute fraction of variance (R2)
"
Root mean square error (RMSE)
N
i¼1
i¼1
N
#
RMSE ¼ ∑ Y imodel −Y actual i
2
, #1=2 N
i¼1
Mean square error (MSE)
i¼1
Mean absolute deviation (MAD)
i¼1
Predicted K'-value
a
Partitioning Coefficient
a 1.2 1 0.8 0.6 0.4 0.2
1.2
Actual Learning
1
Predicted
0.8 0.6 0.4 0.2 0 0
5
10
0 0
0.2
0.4
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Actual K'-value Fig. 2. Predicted partition coefficients plotted against actual data (K′ = K/100). (a) Hybrid GMDH–NN and (b) original GMDH network.
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Data Number Fig. 3. Predicted partition coefficients (K′ = K/100) plotted against data number. (a) Hybrid GMDH–NN and (b) original GMDH network.
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variables are changing. Thus, in the second modification these points are omitted from the data set. In order to unify the order of magnitude of the inputs and outputs, some modifications are performed on them. These modifications are stated in Table 3. In this study, the structure of hybrid GMDH–neural network model was developed with 3 neural inputs in 4 layers, as shown in schematic Fig. 1. As can be seen from the figure, the proposed model has one input layer, two middle layer and one output layer. Moreover, the figure clearly shows some cross overs between nodes in different layers which is the distinct characteristic of hybrid GMDH–NN model. Generated functions corresponding to each node in each layer along with total correlation function are represented in Table 3. The actual and predicted results together with related Average Absolute Deviations Percent (% AAD) are reported in Table 4. Moreover, Table 5 demonstrates the differences between original and hybrid GMDH model. The general formula for the calculation of %AAD is given in Eq. (13):
%AAD ¼
N model 100 X −Y actual Y i i actual N i¼1 Yi
ð13Þ
Table 5 clearly shows the reliability and accuracy of the proposed hybrid GMDH–NN model in predicting partitioning of alkaloids in IL-based ABS in comparison with original one. Moreover, the experimental and predicted K-values are compared in Figs. 2 and 3. As can be observed from the figures, the results of the proposed model are in good agreement with the experimental data as many of the data points fall very close to diagonal line. However, original GMDH is unable to predict the variation of K-value as the function of inputs. Some statistical measures can be used for determining the model's accuracy and reliability. These statistical values can be defined as shown in the Table 4 and their values are calculated based on the output of the network. 4. Conclusion As it was observed, hybrid GMDH–NN was used in order to estimate partition coefficients of two alkaloids in ABS based on different ILs and the same inorganic salt. The model was developed in 4 layers with 3 inputs in each layer. Schematic diagram of the proposed model showed some cross overs between layers which are, as stated, the distinct characteristic of hybrid GMDH–NN. Furthermore, comparison of the estimated K-values with experimental results, as demonstrated in tables and figures, showed excellent agreements among them. Some statistical measures were also used in order to estimate the model's accuracy. Their calculated values fitted well among their standard values and thus proposing reliability of the model. Moreover, %AAD was calculated to be 8.78% which
was a desired value in statistical measures. Hence, the closeness of the predicted and experimental K-values demonstrates that the model can efficiently predict alkaloid's partitioning in IL-based ABS at 298.15 K. The proposed model shows how different process variables influence K-values of alkaloid in IL-based ABS. Indeed, changing the type of ABS system would change the final equation but the core structure of the model is unchanged. Thus, the proposed model gives an insight into the influencing parameters and can be used as the basis for modeling of other types of ABS. References [1] P.A. Albertsson, Partitioning of Cell Particles and Macromolecules, Third ed. Wiley-Interscience, New York, 1986. [2] R.K. Scopes, Protein Purification: Principles and Practice, Third ed. Springer-Verlag, Berlin, 1994. [3] B.Y. Zaslavsky, Aqueous Two-Phase Partitioning—Physical Chemistry and Bioanalytical Applications, Marcel Dekker, New York, 1995. [4] K.E. Gutowski, G.A. Broker, H.D. Willauer, J.G. Huddleston, R.P. Swatloski, J.D. Holbrey, R.D. Rogers, J. Am. Chem. Soc. 125 (2003) 6632. [5] M.G. Freire, A.M. Claudio, J.M.M. Araujo, A.P. Coutinho, I.M. Marrucho, I.M. Canongia Lopes, P.N. Rebelo, Soc. Rev. 41 (2012) 4966. [6] S. Dreyer, P. Salim, U. Kragl, Biochem. Eng. J. 46 (2009) 176. [7] P.P. Madeira, X. Xu, J.A. Teixeira, E.A. Macedo, Biochem. Eng. J. 24 (2005) 147. [8] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Z. Phys. Chem. 223 (2009) 263. [9] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Ind. Eng. Chem. Res. 48 (2009) 4109. [10] A.D. Diamond, J.T. Hsu, Biotechnol. Bioeng. 34 (1989) 1000. [11] A.D. Diamond, J.T. Hsu, J. Chromatogr. B 513 (1990) 137. [12] A.D. Diamond, J.T. Hsu, AlChE Symp. Ser. 88 (1992) 105. [13] S. Ganguly, J. Comput. Chem. Eng. 27 (2003) 1445. [14] S. Ketabchi, H. Ghanadzadeh, A. Ghanadzadeh, S. Fallahi, M. Ganji, J. Chem. Thermodyn. 42 (2010) 1352. [15] S.Z. Reyhani, H. Ghanadzadeh, L. Puigjaner, F. Recances, J. Ind. Eng. Chem. Res. 48 (2009) 2129. [16] F.S. Mjalli, J. Chem. Eng. Sci. 60 (2005) 239. [17] J.S. Torrecilla, M. Deetlefs, J. Chem. Phys. 10 (2008) 5114. [18] S. Bogdan, D. Gosak, D. Vasic-Racki, Comput. J. Chem. Eng. 19 (1995) 791. [19] J. Park, I. Sandberg, J. Neural Comput. 3 (1991) 246. [20] M.J.D. Powell, in: J.C. Mason, M.G. Cox (Eds.), Radial Basis Functions for Multivariable Interpolation: A Review in Algorithms for Approximation, Clarendon Press, Oxford, UK, 1987, p. 143. [21] N. Nariman-Zadeh, A. Jamali, in: J. Drchal, J. Koutnik (Eds.), Proceedings of the International Workshop on Inductive Modelling, Czech Technical University, Prague, Czech Republic, 2007, p. 96. [22] A.G. Ivakhnenko, IEEE Trans. Syst. Man Cybern. 1 (1971) 364. [23] H. Ghanadzadeh, M. Ganji, S. Fallahi, Appl. Math. Model. 36 (2012) 4096. [24] G.C. Onwubolu, Hybrid Self-Organizing Modeling Systems, Springer, Berlin, 2009. [25] P. Kan, C.J. Lee, Ind. Eng. Chem. Res. 35 (1996) 2015. [26] G. Gautam, L. Simon, Chem. Eng. Commun. 194 (2007) 117. [27] G.R. Pazuki, V. Taghikhani, M. Vossoughi, Part. Sci. Technol. 28 (2010) 67. [28] G.R. Pazuki, S. Seyfi Kakhki, J. Mol. Liq. 188 (2013) 133. [29] M.G. Freire, C.M.S.S. Neves, I.M. Marrucho, J.N. Lopes, L.P. Rebelo, J.A.P. Coutinho, Green Chem. 12 (2010) 1715. [30] C.M.S.S. Neves, S.P.M. Ventura, M.G. Freire, I.M. Marrucho, J.A.P. Coutinho, J. Phys. Chem. B 113 (2009) 5194. [31] S.P.M. Ventura, C.M.S.S. Neves, M.G. Freire, I.M. Marrucho, J. Oliveira, J.A.P. Coutinho, J. Phys. Chem. B 113 (2009) 9304. [32] A.G. Ivakhnenko, Sov. Autom. Control 13 (1966) 43.